Question

algebraic exterior angles
due mar 26, 2026 by 11:59pm points 100
submitting an external tool
assignment overview 1
score: 1/8 penalty: 1 off
exterior angles of polygons
question video examples
the measures of the exterior angles of a triangle are ( 5 x ^ { circ } ), ( 9 x ^ { circ } ), and ( 10 x ^ { circ } ). find the measure of the largest exterior angle.
answer
attempt 1 out of 2
submit answer

Explanation:

Step1: Use the exterior angle sum property

The sum of the exterior angles of any polygon is \(360^{\circ}\). For a triangle (a 3 -sided polygon), we have the equation \(5x + 9x+10x=360\).

Step2: Combine like terms

Combine the \(x\) - terms: \((5 + 9+10)x=360\), so \(24x = 360\).

Step3: Solve for \(x\)

Divide both sides of the equation \(24x = 360\) by 24: \(x=\frac{360}{24}=15\).

Step4: Find the largest exterior angle

The exterior angles are \(5x\), \(9x\), and \(10x\). Since \(10>9 > 5\), substitute \(x = 15\) into \(10x\). So \(10x=10\times15 = 150\).

Answer:

\(150\)